Effect size is "a measure of the strength of a phenomenon or a sample-based estimate of that quantity" [Wikipedia].
Effect size is a measure for the strength of a phenomenon. When calculated from data, it is a descriptive statistic which estimates the magnitude of a relationship.
The minimum size of an effect that can be detected by a specific statistical testing procedure can be calculated as the "minimum detectable difference" (MDD) for a fixed test level $\alpha$ and power $\lambda$. The MDD is often calculated before carrying out an experiment to determine whether it is worthwhile to run the experiment at all. The effect size complements statistical tests and plays an important role in meta and power analyses.